MAZUR (1998)

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185
JOURNAL OF THE EXPERIMENTAL ANALYSIS OF BEHAVIOR 1998, 69, 185–197 NUMBER 2 (MARCH)
PROCRASTINATION BY PIGEONS WITH
FIXED-INTERVAL RESPONSE REQUIREMENTS
JAMES E. MAZUR
SOUTHERN CONNECTICUT STATE UNIVERSITY
Two experiments studied the phenomenon of procrastination, in which pigeons chose a larger, more
delayed response requirement over a smaller, more immediate response requirement. The response
requirements were fixed-interval schedules that did not lead to an immediate food reinforcer, but
that interrupted a 55-s period in which food was delivered at random times. The experiments used
an adjusting-delay procedure in which the delay to the start of one fixed-interval requirement was
varied over trials to estimate an indifference point—a delay at which the two alternatives were chosen
about equally often. Experiment 1 found that as the delay to a shorter fixed-interval requirement
was increased, the adjusting delay to a longer fixed-interval requirement also increased, and the rate
of increase depended on the duration of the longer fixed-interval requirement. Experiment 2 found
a strong preference for a fixed delay of 10 s to the start of a fixed-interval requirement compared
to a mixed delay of either 0 or 20 s. The results help to distinguish among different equations that
might describe the decreasing effectiveness of a response requirement with increasing delay, and
they suggest that delayed reinforcers and delayed response requirements have symmetrical but op-
posite effects on choice.
Key words: choice, fixed-interval schedules, delay, procrastination, key peck, pigeons
A long-standing question is whether rein-
forcers and punishers have symmetrical but
opposite effects on behavior (e.g., Deluty,
1976; de Villiers, 1980; Rachlin & Herrnstein,
1969; Thorndike, 1932). Evidence that they
do comes from a variety of experiments that
have shown that variables such as delay, mag-
nitude, rate, and schedule of delivery have
similar effects for reinforcers and punishers
(see Mazur, 1998, pp. 190–193; Vaughan,
1987). Stated in a slightly different way, the
issue is whether the same general principles
of behavior can be applied to hedonically
positive and negative events.
In the experiments reported here, this
question was investigated by examining pi-
geons’ choices between two different fixed-
interval (FI) response requirements. It was as-
sumed that the FI requirements served as
mild punishers for two reasons: (a) They re-
quired that the pigeons make one or more
responses, but completion of the FI require-
ments were not directly followed by a rein-
forcer; and (b) they interrupted periods in
This research was supported by Grant MH 38357 from
the National Institute of Mental Health. I thank Karyn
Cassello, Kim Mastriano, and Stephen Redente for their
help in various phases of the research.
Correspondence concerning this article should be sent
to James E. Mazur, Psychology Department, Southern
Connecticut State University, New Haven, Connecticut
06515 (E-mail: mazur@scsu.ctstateu.edu).
which food was presented at random times,
so they were, in effect, periods of timeout
from positive reinforcement. A number of
previous studies have shown that avoiding
timeouts from periods of positive reinforce-
ment can be an effective reinforcer for pi-
geons (e.g., Galbicka & Branch, 1983; Hack-
enberg, 1992), which suggests that the
timeouts are aversive events. The purpose of
the present experiments was to determine
whether the effects of two variables, the delay
and magnitude of FI requirements, are simi-
lar to the effects of delay and magnitude of
positive reinforcement.
Mazur (1996) used the term procrastination
to refer to cases in which subjects chose a
larger, more delayed response requirement
over a smaller, more immediate response re-
quirement. In three experiments, pigeons
showed a strong tendency to choose a larger
response requirement if its onset was delayed
a few seconds. For instance, in one of the ex-
periments, the pigeons were presented with
discrete trials in which response-independent
food was delivered according to a variable-
time (VT) 20-s schedule. At some point in
each trial, the VT schedule was interrupted,
and a fixed-ratio (FR) requirement had to be
completed. Completion of the FR require-
ment did not lead to an immediate reinforc-
er, but simply allowed the VT schedule to re-
sume. In this choice procedure, the pigeons
186 JAMES E. MAZUR
could choose between completing a small FR
requirement early in the trial or a larger FR
requirement later in the trial. All subjects
clearly exhibited procrastination, choosing a
larger, more delayed response requirement
over a smaller, more immediate response re-
quirement. In some conditions, the birds
showed a preference for the more delayed re-
sponse requirement even when it was more
than four times larger than the more imme-
diate response requirement.
Mazur (1996) suggested that the pigeons’
choices in these experiments were similar to
those of animals in self-control choice situa-
tions, in which subjects must choose between
a small, more immediate reinforcer and a
larger, more delayed reinforcer. In self-con-
trol choice situations, animals often show a
preference for the smaller, more immediate
reinforcer (e.g., Ainslie, 1974; Green, Fisher,
Perlow, & Sherman, 1981; Rachlin & Green,
1972), and in the procrastination experi-
ments, they showed a preference for the larg-
er, more delayed response requirement, but
the parallel is straightforward: In both cases,
with increasing delay, the larger event
(whether positive or negative) had less and
less effect on a subject’s behavior.
The parallel between delayed positive and
negative events would be more compelling if
it turned out that the effects of delay can be
described by the same mathematical expres-
sion in both cases. A variety of experiments
have suggested that as a reinforcer’s delay in-
creases, its value (its ability to sustain instru-
mental responses) declines according to the
following equation:
A
V 5 , (1)
1 1 K D
where V is the value of a reinforcer delivered
after a delay of D seconds, A is a parameter
related to the amount of reinforcement, and
K is a parameter that determines how rapidly
V decreases with increases in delay. Because
Equation 1 describes a hyperbola, it has been
called the hyperbolic decay model.
One study that provided support for this
model used pigeons in a self-control choice
procedure (Mazur, 1987). On each trial, a pi-
geon chose between a standard alternative,
which delivered 2 s of access to grain after a
fixed delay, and an adjusting alternative,
which delivered 6 s of access to grain after a
delay that increased or decreased over trials
depending on the subject’s choices. The pur-
pose of these adjustments was to estimate an
indifference point, or a delay at which the
two alternatives were chosen about equally of-
ten. The standard delay was varied across con-
ditions, and for each standard delay, an in-
difference point was obtained. If we assume
that, at an indifference point, Vs 5 Va (where
the subscripts refer to the standard and ad-
justing alternatives), solving for Da in Equa-
tion 1 yields the following:
D 5 (A 2 A )/K A 1 (A /A )D . (2)a a s a a s s
Equation 2 states that as the standard delay
increases, the equivalent adjusting delay at
the indifference point should increase ac-
cording to a linear function with a slope of
Aa/As and a positive y intercept of (Aa 2 As)/
KAa. Mazur (1987) found that the results
from all 4 pigeons were consistent with this
prediction. In addition, the results were in-
consistent with other possible decay equa-
tions, including an exponential equation (V
5 Ae - KD) and a simple reciprocal equation (V
5 A/KD). Other studies have found similar
results (e.g., Green, Fry, & Myerson, 1994;
Rodriguez & Logue, 1988), and Grossbard
and Mazur (1986) also found a linear relation
when fixed and adjusting ratio schedules
were used instead of fixed and adjusting de-
lays.
It may be possibleto apply these same
equations to choices involving aversive events
that vary in delay and amount, in the follow-
ing way. Suppose V now represents the neg-
ative value of a delayed aversive event, such
as a response requirement. A is now a mea-
sure of the size of the response requirement,
and D represents the delay between a choice
response and the onset of the response re-
quirement. (For a similar suggestion about a
quantitative parallel between positive rein-
forcement and punishment, see Vaughan,
1987.) If a subject is given a choice between
a small response requirement that begins af-
ter a short delay and a larger response re-
quirement that begins after an adjusting de-
lay, Equations 1 and 2 predict the same
pattern as for positive reinforcement. To be
specific, if the mean adjusting delays (indif-
ference points) are plotted as a function of
the delays to the small response requirement
187PROCRASTINATION WITH FI SCHEDULES
(which are varied across conditions), the re-
sults should be a straight line with a slope
greater than 1 and a y intercept greater than
0. The simple reciprocal equation also pre-
dicts a slope greater than 1, but it predicts a
y intercept of 0. Both of these equations also
predict that the slope of the indifference
function should vary as a function of the rel-
ative sizes of the two response requirements.
In contrast, the exponential equation pre-
dicts that the indifference function will have
a slope of 1 regardless of the sizes of the two
response requirements.
Experiment 1 was designed to extend Ma-
zur’s (1996) research on the procrastination
effect to somewhat different choice situa-
tions, and to collect data that might help to
determine which decay equation best de-
scribes how the effect of a response require-
ment decreases as its delay increases. The
procedure differed from the one used by Ma-
zur (1996) in at least two ways. In the previ-
ous study, the size of the larger response re-
quirement was adjusted over trials to estimate
an indifference point. In the present experi-
ment, the response requirements were held
constant, and the delay to the larger response
requirement was adjusted over trials. This
procedure therefore more closely resembled
the adjusting-delay procedure that has been
used in several studies with positive reinforc-
ers (e.g., Mazur, 1987, 1988; Rodriguez &
Logue, 1988). Second, whereas Mazur (1996)
used FR schedules as the two response re-
quirements, FI schedules were used in the
present experiment. These FI schedules
served as timeouts from positive reinforce-
ment, but they were short in duration and
were probably only mildly aversive. It was
therefore not certain how much control they
would exert over the pigeons’ choice re-
sponses. However, if the magnitudes and de-
lays of the FI requirements had any orderly
effects on choice, the results might at least
distinguish between the exponential equation
(which predicts that the indifference func-
tions will have slopes equal to 1) and equa-
tions that predict that the slopes will be great-
er than 1 (e.g., the hyperbolic and reciprocal
equations).
The purpose of Experiment 2 was to ex-
amine another possible parallel between pos-
itive and negative delayed events. A number
of studies have found that animals exhibit a
strong preference for variable delays to rein-
forcement over fixed delays (e.g., Cicerone,
1976; Rider, 1983), and Mazur (1984) showed
that a variation of Equation 1 can account for
this effect. Experiment 2 compared pigeons’
choices between fixed and variable delays to
the onsets of equal FI requirements. As will
be explained below, if the same principles ap-
ply, subjects should show an avoidance of vari-
ability with aversive events rather than the
preference for variability that is found with
positive reinforcers.
EXPERIMENT 1
In this experiment, pigeons chose between
an FI 5-s schedule after a fixed delay and an
FI 15-s schedule (or, in some conditions, an
FI 7.5-s schedule) after an adjusting delay. In
both cases, these FI schedules interrupted a
55-s period in which response-independent
food was delivered at random times (on a VT
20-s schedule). Completion of the FI require-
ments did not lead to immediate food, but
simply allowed the VT schedule to resume.
For both the standard and adjusting alterna-
tives, the VT schedule was in effect for a total
of 55 s every trial, so the only differences be-
tween the alternatives were (a) the size of the
FI schedule and (b) the delay from a choice
response to the onset of the FI schedule.
Method
Subjects. Three White Carneau pigeons
were maintained at about 80% of their free-
feeding weights. All had previous experience
with a variety of experimental procedures. A
4th pigeon received a few conditions but then
became ill, and it was removed from the ex-
periment.
Apparatus. The experimental chamber was
30 cm long, 30 cm wide, and 33 cm high.
Three response keys, each 1.8 cm in diame-
ter, were mounted in the front wall of the
chamber, 20.5 cm above the floor. A force of
approximately 0.15 N was required to operate
each key, and each effective response pro-
duced a feedback click. Each key could be
transilluminated with lights of different col-
ors. A hopper below the center key provided
controlled access to grain, and when grain
was available, the hopper was illuminated
with a 2-W white light. Six 2-W lights (two
white, two red, two green) were mounted
188 JAMES E. MAZUR
Fig. 1. The consequences of a choice of the green or red keys are shown for Condition 1 of Experiment 1.
above the wire-mesh ceiling of the chamber.
The chamber was enclosed in a sound-atten-
uating box that contained a ventilation fan.
All stimuli were controlled and responses re-
corded by an IBM-compatible personal com-
puter using the Medstatet programming lan-
guage.
Procedure. The experiment consisted of 13
conditions. In all conditions, each session
lasted for 48 trials or for 60 min, whichever
came first. Each block of four trials consisted
of two forced trials followed by two choice
trials. At the start of each trial, the white
houselights were lit, and the center key was
transilluminated with white light. A single
peck on the center key was required to begin
the choice period. The purpose of this cen-
ter-key peck was to make it more likely that
the subject’s head was equidistant from the
two side keys when the choice period began.
On choice trials, a peck on the center key
darkened this key and illuminated the two
side keys, one key green and the other red.
The positions of the two key colors were var-
ied randomly over trials. A single peck on the
green key constituted a choice of the stan-
dard alternative, and a single peck on the red
key constituted a choice of the adjusting al-
ternative.
To illustrate the general procedure, Figure
1 shows the two possible sequences of events
that could occur in Conditions 1, 8, and 13.
For both alternatives, a VT 20-s schedule was
in effect for a total of 55 s each trial (includ-
ing the durations of the reinforcer presenta-
tions), but this 55-s period was interrupted at
some point, and an FI requirement had to be
completed before the VT schedule resumed.
In these three conditions, each choice of the
green (standard) key led to (a) offset of the
two keylights and the white houselights, onset
of the green houselights, and a 10-s segment
(which will be called the standard delay) in
which the VT schedule was in effect; (b) off-
set of the green houselights and onset of the
green keylight and white houselights, which
remained on until the subject completed an
FI 5-s schedule; and (c) offset of the green
keylight and white houselights, onset of the
green houselights, and a 45-s segment with
the VT schedule in effect. (In other condi-
tions, the standard delay was different, but
the durations of the two VT segments always
summed to 55 s.)
Each choice of the red (adjusting) key led
to (a) offset of the two keylights and the white
houselights, onset of the red houselights, and
a segment ofadjusting duration (which will
be called the adjusting delay) in which the VT
20-s schedule was in effect; (b) offset of the
red houselights and onset of the red keylight
and white houselights, which remained on
until the subject completed an FI 15-s sched-
ule; and (c) offset of the red keylight and
white houselights, onset of the red house-
lights, and a second segment with the VT
schedule in effect. As with the standard alter-
native, the durations of the two VT segments
summed to 55 s on each trial. However, their
individual durations typically increased and
decreased several times a session, as ex-
plained below.
189PROCRASTINATION WITH FI SCHEDULES
Table 1
Order of conditions in Experiment 1. All durations are
in seconds.
Condition Adjusting FI Standard delay
1
2
3
4
5
6
7
15
15
15
15
15
15
15
10
0
7
4
0
7
4
8
9
10
11
12
13
15
7.5
7.5
7.5
7.5
15
10
10
0
7
4
10
Whenever the VT schedule delivered a re-
inforcer, the colored houselights were extin-
guished, the white light in the food hopper
was lit, and grain was presented for a maxi-
mum of 2 s. However, if a VT segment was
scheduled to end before the 2-s reinforce-
ment period was over, the reinforcement pe-
riod was shortened accordingly, to keep the
durations of the VT segments exactly as
scheduled.
The procedure on forced trials was the
same as on choice trials, except that only one
side key was lit (red or green), and a peck on
this key led to the sequence described above.
A peck on the opposite key, which was dark,
had no effect. Of every two forced trials, one
involved the red key and the other involved
the green key. The temporal order of these
two types of trials varied randomly.
After every two choice trials, the duration
of the adjusting delay might be changed. If a
subject chose the standard key on both
choice trials, the adjusting delay was in-
creased by 1 s (up to a maximum of 40 s). If
the subject chose the adjusting key on both
trials, the adjusting delay was decreased by 1
s. If the subject chose each key on one of the
two trials, no change was made. In all three
cases, this adjusting delay remained in effect
for the next block of four trials. At the start
of the first session of each condition, the ad-
justing delay was equal to the standard delay.
At the start of later sessions of the same con-
dition, the adjusting delay was determined by
the above rules as if it were a continuation of
the preceding session.
In all conditions, the standard alternative
included an FI 5-s schedule. Table 1 shows
that in nine conditions, the adjusting alter-
native included an FI 15-s schedule, and in
the other four conditions the adjusting alter-
native included an FI 7.5-s schedule. Table 1
also shows that in different conditions, the
standard delay was set at either 0, 4, 7, or 10
s. (In conditions with a 0-s standard delay, the
FI 5-s schedule began immediately after a
choice response on the green key, and it was
followed by a 55-s segment with the VT sched-
ule in effect.)
Conditions 1 and 9 lasted for a minimum
of 20 sessions, and all other conditions lasted
for a minimum of 14 sessions. After the min-
imum number of sessions, a condition was
terminated for each subject individually when
several stability criteria were met. To assess
stability, each session was divided into two 24-
trial blocks, and for each block the mean ad-
justing delay was calculated. The results from
the first two sessions of a condition were not
used, and the condition was terminated when
all of the following criteria were met, using
the data from all subsequent sessions: (a) Nei-
ther the highest nor the lowest single-block
mean of a condition could occur in the last
six blocks of a condition. (b) The mean ad-
justing delay across the last six blocks could
not be the highest or the lowest six-block
mean of the condition. (c) The mean delay
of the last six blocks could not differ from
the mean of the preceding six blocks by more
than 10% or by more than 1 s (whichever was
larger).
Results
The number of sessions needed to meet
the stability criteria ranged from 14 to 31
(median 5 17 sessions). To illustrate the
changes that occurred in the adjusting delay
within a condition, Figure 2 presents the trial-
by-trial durations of the adjusting delay for
each subject in Conditions 8 and 9. The stan-
dard delay was 10 s in both of these condi-
tions, but the FI for the adjusting alternative
was 15 s in Condition 8 and 7.5 s in Condition
9. Figure 2 shows that in some cases (e.g.,
Subjects 1 and 2 in Condition 8), the adjust-
ing delay showed a relatively steady progres-
sion from its original duration of 10 s to its
duration at the end of the condition. How-
ever, in other cases (e.g., Subject 3 in Con-
190 JAMES E. MAZUR
Fig. 2. Trial-by-trial variations in the adjusting delays are shown for each subject from Conditions 8 and 9. A
vertical line in each panel marks the six half-session blocks that satisfied the stability criteria.
dition 9), the changes in the adjusting delay
were more erratic, and the adjusting delay
continued to show large variations at the end
of the condition, when the stability criteria
were met. Figure 2 also shows one likely in-
stance of a ceiling effect (Subject 3 in Con-
dition 8), because the adjusting delay
reached the maximum possible duration of
40 s in Session 23, and it remained close to
40 s for the remainder of the condition.
All subsequent data analyses were based on
the results from the six half-session blocks
that satisfied the stability criteria in each con-
dition. For each subject and each condition,
the mean adjusting delay from these six half-
session blocks will be called the indifference
point. In Figure 3, the indifference points are
plotted as a function of the standard delay for
each of the 13 conditions. The first thing to
note is that there was much more variability
191PROCRASTINATION WITH FI SCHEDULES
Fig. 3. The mean adjusting delays from each condition are plotted as a function of the standard delays for each
subject and for the group means in Experiment 1. Different symbols are used to identify the two or three replications
of the FI 15-s conditions.
between and within subjects than has been
found in similar studies with positive rein-
forcers (e.g., Mazur, 1987; Rodriguez &
Logue, 1988). The indifference points in Ma-
zur’s (1996) previous study on procrastina-
tion were also quite variable, and possible rea-
sons for this variability will be discussed
below. There were also several instances of
possible ceiling effects, where the mean ad-
justing delay was close to its maximum value
of 40 s.
Despite the variability in the indifference
points from individual conditions, two trends
are evident in Figure 3. First, as the standard
delay increased from 0 s to 10 s, the mean
adjusting delay also increased, in both the FI
15-s and FI 7.5-s conditions. Second, these in-
creases in the adjusting delay were much larg-
er in the FI 15-s conditions than in the FI 7.5-
s conditions. This difference between the FI
15-s and FI 7.5-s conditions is consistent with
both the hyperbolic and reciprocal equations,
because they predict that the rate of increase
in the adjusting delay will depend on the rel-
ative sizes of the two FI requirements. It is not
consistent with the exponential equation,
which predicts that the adjusting delay will
increase at the same rate (with a slope of 1)
regardless of the sizes of the two FI require-
ments.
For each subject, one regression line was
fitted to the indifference points from the FI
15-s conditions, and a second line was fitted
to the indifference points from the FI 7.5-s
192 JAMES E. MAZUR
Table 2
Slopes, y intercepts, and percentages of variance account-
ed for (%VAC) for regression lines fitted to the data in
Figure 2.
Bird 1 Bird 2 Bird 3 Mean
FI 15-s conditions
Slope
y intercept
%VAC
2.21
0.0
82.0
3.15
2.9
53.2
4.03
4.7
87.2
3.14
2.0
94.9
FI 7.5-s conditions
Slope
y intercept
%VAC
0.81
3.5
33.9
0.69
0.3
99.0
1.25
4.6
32.4
0.922.7
68.9
conditions. Table 2 shows the results of these
regression analyses. For the FI 15-s condi-
tions, the slopes of the regression lines were
much greater than 1 for all subjects; this is
also consistent with the hyperbolic and recip-
rocal equations but is inconsistent with the
exponential equation. The slopes for the FI
7.5-s conditions were closer to 1, and were in
fact less than 1 for 2 subjects. According to
the hyperbolic and reciprocal equations, the
slopes should be greater than 1 because the
FI 7.5-s schedule for the adjusting alternative
was larger than the FI 5-s schedule of the stan-
dard alternative. The low slopes might reflect
a bias toward the adjusting alternative, be-
cause in this procedure such a bias would
tend to decrease the indifference points.
As demonstrated in Equation 2, the hyper-
bolic equation predicts that the y intercept
should be positive and should increase as the
size of the larger response requirement in-
creases relative to the smaller response re-
quirement. In contrast, the simple reciprocal
equation predicts a y intercept of zero re-
gardless of the sizes of the two response re-
quirements. Because of the variability in the
data and the possibility of ceiling effects, the
y intercepts shown in Table 2 must be viewed
with caution. However, Table 2 shows that five
of six y intercepts for individual subjects were
positive, and the sixth was zero.
Another way to address this matter is to ex-
amine the indifference points from only
those conditions with a standard delay of 0 s.
Of course, the mean adjusting delays could
not go below 0 s, but for each subject they
were slightly larger in both of the FI 15-s con-
ditions with a 0-s standard delay (M 5 1.8 s)
than in the one FI 7.5-s condition with a 0-s
standard delay (M 5 0.6 s). This small but
consistent difference provides some evidence
that even with a standard delay of 0 s, the
indifference points were sensitive to the sizes
of the two FI requirements.
Discussion
The results indicate that pigeons’ choices
between two delayed FI requirements are af-
fected by magnitude and delay in ways that
are similar to their choices between two de-
layed reinforcers. The rising functions in Fig-
ure 2 suggest that as the delay to the start of
an FI requirement increased, the FI require-
ment had progressively less effect on a sub-
ject’s choice response. The different results
from the FI 7.5-s and FI 15-s conditions are a
clear indication that the pigeons’ choices
were controlled by the sizes of the two FI re-
quirements as well as by their delays.
The differences in the slopes between the
FI 7.5-s and FI 15-s conditions are consistent
with the prediction of the hyperbolic and re-
ciprocal equations, but they are inconsistent
with the prediction of the exponential equa-
tions that the slopes should always equal 1.
The fact that the slopes for the FI 15-s con-
ditions were much greater than 1 are further
evidence favoring the hyperbolic and recip-
rocal equations over the exponential equa-
tion. However, the hyperbolic and reciprocal
equations also predict that the slopes should
be greater than 1 for the FI 7.5-s conditions,
whereas Table 2 shows that the slopes were
less than 1 for 2 subjects and just slightly
greater than 1 for the 3rd. One possible rea-
son why these slopes were not steeper is that
they might have been decreased by either a
color bias or a bias toward the adjusting al-
ternative. In previous studies with the adjust-
ing-delay procedure and positive reinforcers,
Mazur (1984, 1995) found a bias for the ad-
justing alternative, which appeared as slopes
that were slightly larger than predicted. With
the procedure used in the present experi-
ment, a bias toward the adjusting alternative
would produce decreased slopes (because ev-
ery two consecutive choices of the adjusting
alternative decreased the adjusting delay).
Because of the variability in the indiffer-
ence points, the results do not offer conclu-
sive evidence that the hyperbolic equation
(which has been successfully applied to posi-
tive reinforcers) made better predictions
193PROCRASTINATION WITH FI SCHEDULES
than the simple reciprocal equation. Two
small pieces of evidence favor the hyperbolic
equation: (a) The y intercepts were greater
than zero for five of the six regression lines
fitted to the indifference points, and (b) the
indifference points from the conditions with
0-s standard delay were consistently greater in
the FI 15-s conditions than in the FI 7.5-s con-
ditions. It is, of course, possible that the in-
difference points from the 0-s delay condi-
tions were influenced by floor effects. When
the adjusting delay was 0 s, two consecutive
choices of the standard alternative would in-
crease the adjusting delay, whereas two con-
secutive choices of the adjusting alternative
could not decrease the delay below 0 s.
Therefore, any variability in the adjusting de-
lay would necessarily produce indifference
points greater than 0 s. However, there is no
obvious reason why this variability would pro-
duce larger indifference points in the FI 15-
s conditions than in the FI 7.5-s conditions if
the actual y intercepts were zero in both
cases, as predicted by the reciprocal equation.
Therefore, the differences between the FI 15-
s and FI 7.5-s conditions tend to favor the
hyperbolic equation over the simple recipro-
cal equation.
It is not clear why the indifference points
were more variable in this experiment, and
in Mazur’s (1996) previous studies on pro-
crastination, than in studies with the adjust-
ing-delay procedure and positive reinforcers
(Mazur, 1987; Rodriguez & Logue, 1988).
One possible explanation is that because of
the many events that occurred on each trial,
learning the consequences that followed
choices of the standard and adjusting alter-
natives was inherently more difficult. In the
studies with delayed positive reinforcers, each
trial had a single delay followed by a single
reinforcer. In the present experiment, each
choice response led to (a) a period in which
zero, one, or several reinforcers might be pre-
sented; (b) an FI requirement; and (c) a sec-
ond period in which zero, one, or several re-
inforcers might be presented. The greater
variability in the indifference points might
simply reflect the greater variability and un-
certainty in the consequences for the two
choice alternatives.
Another possible reason for the greater
variability in the data is that the delayed FI
requirements were simply not as powerful as
delayed food presentations in their control
over choice behavior. Previous studies with pi-
geons have found only small differences in
preference (or none at all) between periods
of key pecking and equally long delays in
which no key pecking is required (Mazur,
1986; Neuringer & Schneider, 1968). It is
true that the FI requirements in the present
experiment were also periods of timeout
from positive reinforcement, but the dura-
tions of these periods (5 to 15 s) were not
long compared to the interreinforcement in-
tervals that normally occurred when the VT
schedules were in operation. In short, these
FI requirements were probably only weakly
aversive, and for that reason they may not
have exerted consistent control over the pi-
geons’ choice responses. Yet considering that
these were probably weak aversive stimuli, the
degree of orderliness in the data is impres-
sive.
EXPERIMENT 2
To make predictions for choices involving
both fixed and variable delays to positive re-
inforcement, Mazur (1984) used the follow-
ing extension of the hyperbolic equation:
n A
V 5 P , (3)O i1 21 1 K Di51 i
where V is now the value of the variable
alternative, which could deliver any one of n
possible delays on any given trial, and Pi is
the probability that a delay of Di seconds will
occur. This equation states that the value of
a variable delay is an average of the values of
all of its component delays, each weighted by
its probability of occurrence. Because the hy-
perbolic equation predicts that reinforcersdelivered after short delays have very high val-
ues, this equation predicts a strong prefer-
ence for a reinforcer delivered after a vari-
able delay (e.g., a delay that could be either
2 or 18 s) over an identical reinforcer deliv-
ered after a fixed delay with the same mean
duration (e.g., a delay of 10 s).
When applied to delays before a response
requirement rather than delays before a re-
inforcer, Equation 3 predicts a strong pref-
erence for fixed over variable delays, because
the shorter delays that sometimes occur with
the variable alternative will have large negative
194 JAMES E. MAZUR
Fig. 4. The mean adjusting delays are plotted for each subject and for the group means from the four conditions
of Experiment 2.
values that the subjects will tend to avoid.
This prediction is not unique to the hyper-
bolic equation. Preference for fixed over vari-
able delays would also be predicted if an ex-
ponential function, a reciprocal function, or
any other decreasing concave upward func-
tion replaced the hyperbolic function in
Equation 3.
Experiment 2 used the same type of ad-
justing-delay procedure as Experiment 1, ex-
cept that the response requirement was FI 10
s for both alternatives. The standard alterna-
tive included a fixed delay (10 s) to the start
of the FI requirement in some conditions and
a variable delay (either 0 s or 20 s) in other
conditions. Note that the mean delay to the
start of the FI requirement was 10 s in both
cases. The predicted preference for fixed
over variable delays should appear as longer
mean adjusting delays in the conditions with
fixed delays for the standard alternative.
Method
Subjects. Four White Carneau pigeons
(none from Experiment 1) were maintained
at about 80% of their free-feeding weights.
All had previous experience with a variety of
experimental procedures.
Apparatus. The experimental chamber had
the same dimensions and features as the one
used in Experiment 1, and the same comput-
er and programming language were used.
Procedure. The procedure was the same as
in Experiment 1, with the following excep-
tions. The experiment consisted of four con-
ditions. An FI 10-s schedule was used for both
the standard and adjusting alternatives in all
conditions. In Conditions 1 and 3, the stan-
dard delay to the start of the FI schedule was
always 10 s. In Conditions 2 and 4, the stan-
dard delay to the start of the FI schedule was
either 0 s or 20 s, and each delay occurred
with equal probability. As in Experiment 1,
for both alternatives a VT 20-s schedule was
in effect for a total of 55 s on each trial.
Each condition lasted for a minimum of 14
sessions, and the same stability criteria as in
Experiment 1 were used to terminate condi-
tions. For Subject 3 in Condition 3, visual in-
spection of the data suggested that the ad-
justing delay was not stable when the criteria
were first met, so the condition was contin-
ued for this subject for another 10 sessions
and until the stability criteria were again met.
Results
The number of sessions needed to meet
the stability criteria ranged from 14 to 48
(median 5 19 sessions). All data analyses
were based on the results from the six half-
session blocks that satisfied the stability cri-
teria in each condition. Figure 4 plots the in-
difference points from the four conditions
for each subject and for the group. As in Ex-
195PROCRASTINATION WITH FI SCHEDULES
periment 1, there was substantial variability
between and within subjects. However, with
only one exception (Condition 2 for Subject
2), the mean adjusting delays were always
larger in the conditions with the fixed delay
of 10 s than in those with the mixed delays
of 0 s or 20 s. For the group as a whole, the
mean adjusting delay was 24.9 s in the fixed-
delay conditions and 6.8 s in the mixed-delay
conditions. This difference indicates that
there was a strong preference for the fixed-
delay standard compared to the mixed-delay
standard.
Discussion
The same explanations for the between-
and within-subject variability discussed for Ex-
periment 1 may apply in this experiment.
One unexpected result, however, was that the
indifference points in the fixed-delay condi-
tions were much greater than 10 s, averaging
about 25 s. If these indifference points were
unbiased estimates of the value of the stan-
dard alternative, they should have averaged
about 10 s in the fixed-delay conditions. The
larger indifference points suggest that there
was a bias toward the standard alternative,
which could have been due to a color pref-
erence or to the differences between the stan-
dard and adjusting delays themselves. In con-
trast, there was, if anything, a bias toward the
adjusting alternative in Experiment 1. The
reasons for the different biases are not
known, but Experiment 2 used different pi-
geons in a different chamber.
Despite the apparent bias for the standard
alternative, the differences between the fixed-
delay and mixed-delay conditions were very
large: Indifference points were almost four
times shorter in the mixed-delay conditions.
Similarly large differences between fixed and
mixed delays to food reinforcers were found
by Mazur (1984). In that study, the mean ad-
justing delay was 11.5 s with a fixed standard
delay of 10 s, and the mean adjusting delay
was 1.2 s with a mixed standard delay of ei-
ther 0 or 20 s. Because the rules for increas-
ing and decreasing the adjusting delay were
the opposite of those used in the present ex-
periment, shorter adjusting delays indicated
an increase in preference for the standard al-
ternative in Mazur’s (1984) experiment,
whereas they indicated a decrease in prefer-
ence for the standard alternative in the pres-
ent experiment. In summary, Mazur’s (1984)
results indicated a strong preference for vari-
able delays to the positive reinforcers, but the
present results indicated a strong preference
for fixed delays to the FI response require-
ments.
GENERAL DISCUSSION
A few previous studies have demonstrated
effects of delayed punishers that were sym-
metrical but opposite to those of delayed re-
inforcers. With rats, Deluty (1978) found
preference for a larger more delayed punish-
er over a smaller more immediate punisher,
which is the opposite of the preference for
smaller, more immediate reinforcers that is
frequently found in self-control choice situa-
tions. Deluty, Whitehouse, Mellitz, and Hine-
line (1983) found that providing rats with the
opportunity to make an irreversible precom-
mitment led to more choices of the smaller,
more immediate punisher, just as studies with
positive reinforcement have found that pre-
commitment increases the likelihood of
choosing the larger, delayed reinforcer (e.g.,
Ainslie, 1974; Rachlin & Green, 1972). In a
study by Hineline (1970), rats responded to
postpone shock deliveries, although the total
number of shocks they received was not re-
duced. These earlier studies all used shock as
a punisher, but Mazur (1996) observed simi-
lar effects of delay using what were probably
much milder aversive events—FR response
requirements.
Although the effects of delayed punishers
are opposite to those of delayed reinforcers
at one level of description, they are consistent
with the same general principle: As the delay
to a stimulus increases, that stimulus (wheth-
er hedonically positive or negative) has less
and less effect on choice behavior. The results
of the present experiments found additional
parallels between delayed reinforcers and
punishers. Consistent with a number of stud-
ies on delayed positive reinforcers (e.g., Ma-
zur, 1987; Rodriguez & Logue, 1988), the re-
sults from the FI 15-s conditions of
Experiment 1 found indifference functions
with slopes greater than 1, which provide ev-
idence against an exponential decay func-
tion. The results did not provide enough data
to make a clear distinction between the hy-
perbolic and simple reciprocal equations, but
196 JAMES E. MAZUR
there were some indications that the y inter-
cepts of the indifference functions wereslightly greater than zero and varied with the
sizes of the FI schedules, which is more con-
sistent with the hyperbolic equation. Overall,
the indifference functions shown in Figure 3,
though quite variable, were generally similar
to those obtained with delayed positive rein-
forcers.
Experiment 2 revealed a strong preference
for fixed over variable delays, which is the op-
posite of the strong preference for variable
delays found with positive reinforcers (e.g.,
Cicerone, 1976; Mazur, 1984). Once again,
however, the results with positive and nega-
tive consequences follow the same general
principle: Events that follow the short delays
of a variable schedule have a large effect on
choice, but events that follow longer delays
have less effect. That is, according to Equa-
tion 3 or other similar averaging rules (e.g.,
Killeen, 1982), animals show a preference for
variable delays to positive reinforcers because
of the large positive values of the occasional
reinforcers that are delivered after short de-
lays, but they avoid variable delays to punish-
ers because of the large negative values of the
punishers that are delivered after short de-
lays.
From a practical perspective, it has long
been known that compared to positive rein-
forcement, punishment has several disadvan-
tages that discourage its use in applied set-
tings (Azrin & Holz, 1966). From a
theoretical perspective, however, the available
data suggest that reinforcing and punishing
stimuli have symmetrical and opposite effects
on behavior. The results from the present ex-
periments add to this body of data, and they
suggest that factors such as delay, magnitude,
and variability have similar effects on choice
behavior with both positive and negative
events.
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Received July 7, 1997
Final acceptance November 26, 1997